Estimating the Extent of Racially Polarized Voting in Multicandidate Contests

Abstract

We extend the standard ecological regression methodology for analysis of racial bloc voting in single-member districts in which there is one seat to be filled to cover multimember districts without a numbered-place system. In such multimember districts voters may vote for up to k candidates and not all voters need to cast the same number of votes. These complications render the usual single-equation OLS technique inappropriate. The methodology we propose involves a two-step estimating procedure. The variable that is our principal concern, the proportion of white voters who vote for the black (or other minority) candidate, has its value determined by combining information from each of our two separate estimating equations. Thus we cannot directly obtain a confidence limit for our estimated value of this variable from either of the two equations alone. We derive a value of the standard error of our estimate of this variable by combining formula for the variance of the quotients and sums of two variables of known variance and covariance. We verify that our results are robust by comparing our estimates with those generated by the “seemingly unrelated regression” (SURE) model that is designed to cope with correlated errors in regressions that share in the same independent variables. The methodology we develop has an important application in voting rights litigation challenging the constitutionality of the multimember districts and at-large elections, which are the most common form of election mechanism in U.S. cities.

Get full access to this article

View all access options for this article.

References

BRACE, K. , L. HANDLEY , B. GROFMAN , and R. NIEMI (1986) “What's special about 65%? The mathematics of minority voting equality.” Presented at the annual meeting of the Midwest Political Science Association, Chicago, April.

BULLOCK, C. S. III . (1983) “The effects of redistricting on black representation in southern state legislatures.” Presented at the annual meeting of the American Political Science Association, Chicago, September 1-4.

DUNCAN, O. D. and B. DAVIS (1953) “An alternative to ecological correlation.” Amer. Soc. Rev. 18, 6: 665-666.

GINGLES v. EDMISTEN (1984) 590 F. Supp. 345 (E.D. N.C.).

GOODMAN, L. A. (1953) “Ecological regression and the behavior of individuals.” Amer. Soc. Rev. 18, 6: 663-664.

GOODMAN, L. A. (1959) “Some alternatives to ecological correlation.” Amer. J. of Sociology 64, 6: 610-625.

GROFMAN, B. (1982) “Alternatives to single-member plurality districts: legal and empirical issues.” Policy Studies J. 9, 3: 875-898.

GROFMAN, B. (1985) “Criteria for districting: a social science perspective.” UCLA Law Rev. (October): 77-184.

GROFMAN, B. (1987) “Models of voting,” pp. 31-61 in S. Long (ed.) Micropolitics Annual, Vol. 2. Greenwich, CT: JAI Press.

10.

GROFMAN, B. , J. LOEWEN , and M. MIGALSKI (1986) “Improving ecological regression.” (unpublished manuscript)

11.

GROFMAN, B. , M. MIGALSKI , and N. NOVIELLO (1985) “The totality of circumstances test in Section 2 of the Voting Rights Act: a social science perspective.” Law and Policy 7, 2: 199-223.

12.

GROFMAN, B. and N. NOVIELLO (1984) “An outline for the analysis of racial bloc voting.” Prepared testimony in Gingles v. Edmisten, North Carolina.

13.

KISH, L. (1965) Survey Sampling. New York: John Wiley.

14.

KOUSSER, J. M. (1974) The Shaping of Southern Politics: Suffrage Restriction and the Establishment of the One-Party South, 1880-1910. New Haven: Yale Univ. Press.

15.

LOEWEN, J. (1982) Social Science in the Courtroom. Lexington, MA: Lexington Books.

16.

MILLER, W. L. (1977) Electoral Dynamics in Britain since 1918. London: Macmillan.

17.

NIEMI, R. , J. HILL , and B. GROFMAN (1985) “The impact of multimember districts on party representation.” Legislative Studies Q. 10, 4: 441-455.

18.

Report of the Committee on the Judiciary of the U.S. Senate on S1992 (1982) Government Printing Office.

19.

ROBINSON, W. S. (1950) “Ecological correlations and the behavior of individuals.” Amer. Soc. Rev. 5, 3: 351-357.

20.

THEIL, H. (1971) Principles of Econometrics. New York: John Wiley.

21.

THORNBURG v. GINGLES (1986) 106 S. Ct. 2752.

22.

ZELLNER, A. (1962) “An efficient method of estimating seemingly unrelated regressions and tests for aggregation bias.” J. of the Amer. Stat. Assn. 57: 348-368.